Prime p₀= 2375256287121783281 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 76 2 70 2 16 2 76 2 (?)
a_n: 0 2 30 32 60 62 138 140 210 212 228 230 306 308
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 308
Found by: Landjunge
db: batch=81, k=14, 28 28 76 70 16 76

SPT(16)	2375255111731207747	0 34 42 54 100 142 172 184 210 222 252 294 340 352 360 394	-1175390575534
TPT(14)	2375255143865247569	0 2 30 32 72 74 162 164 228 230 330 332 342 344	-1143256535712
SPT(16)	2375255171840625287	0 12 26 50 96 114 132 162 224 254 272 290 336 360 374 386	-1115281157994
SPT(16)	2375255285587035557	0 2 44 66 80 192 210 212 234 236 254 366 380 402 444 446	-1001534747724
STPT(10)	2375255401221398921	0 2 36 38 78 80 120 122 156 158	-885900384360
SPT(16)	2375256258163486559	0 24 30 44 68 98 114 164 198 248 264 294 318 332 338 362	-28958296722
SPT(16)	2375256460729478917	0 6 24 52 66 84 112 156 160 204 232 250 264 292 310 316	173607695636
SPT(16)	2375256536083122331	0 16 22 40 48 72 132 148 210 226 286 310 318 336 342 358	248961339050
SPT(16)	2375256650314081973	0 18 98 138 140 176 216 218 228 230 270 306 308 348 428 446	363192298692
STPT(10)	2375257340061787001	0 2 6 8 18 20 30 32 36 38	1052940003720
SPT(16)	2375257401245811437	0 12 24 66 104 134 144 150 176 182 192 222 260 302 314 326	1114124028156